The U.S. Pat. Nos. 4,178,537 and 4,253,050 disclose processes wherein a high resolution incremental transmitter of the angle of revolution is connected not only to the workpiece spindle but also to the tool spindle. The faster rotating tool spindle is driven continuously. The angle transmitter assigned to the tool spindle supplies an input to the controller in order to drive the slower rotating workpiece spindle. By appropriate design of the controller and the drive for the workpiece spindle, the workpiece spindle can follow up on the tool spindle in a synchronous manner and at the correct angle.
Of course, arbitrarily high compliance cannot be obtained in this process. However, the control quality that can be obtained determines to a large degree the accuracy of the gear to be machined. Increasing the gain of the circuit is not a solution because, due to the rotating masses that are by necessity in the controlled drive, phase shifts occur automatically in the control path which results in instability at too high a gain in the circuit. Theoretically, of course, it would be possible to obtain the desired behavior with a state controller of high order. This, however, would require complicated calculations of innumerable parameters in very short time intervals in addition to additional extremely accurate and thus expensive transducers. For such controllers neither the mathematics nor the necessary fast computers, which are economically feasible, are currently available.